具有温储备失效和延迟修理的M/G/1可修排队系统的可靠性指标

Reliability indices of M/G/1 repairable queueing system with warm standby failure and delayed repair

本文考虑了具有温储备失效特征的M/G/1可修排队系统.在该系统中,服务台故障分为两类:第一类是服务台在服务员的"广义忙期"中以故障率为α(0≤α<∞)的泊松过程发生故障,第二类是服务台在系统闲期中以分布函数为Y(t)的更新过程发生故障,而且发生第二类故障时不能得到立即修理.利用全概率分解技术和拉普拉斯变换工具,分别讨论了在两类故障模式下服务台的瞬态不可用度和稳态不可用度,(0,t]时间内的平均故障次数和稳态故障频度等可靠性指标,进一步还讨论了服务台由温储备失效引起等待修理的概率.最后,通过数值计算例子讨论了系统有关参数对服务台的第二类稳态不可用度和第二类稳态故障频度的影响.

This paper considers the M/G/1 repairable queuing system with warm standby failure. While the service station is in the course of ＂generalized busy period＂ it is subject to breakdowns （we call this the 1 type failure） according to a Poisson process with rate α（0≤α〈∞）, while the service station is in the system idle period it is subject to breakdowns （we call this the 2 type failure） according to a renewal process with distribution Y（t） and the broken service station don＇t be repaired at once. By using the total probability decomposition technique and the Laplace transform, some reliability indices of the service station, such as the transient-state and steady-state unavailability, the expected failure number during （0,t] and so on, are studied under two failed states. Further, a new index which is the waiting repair probability of the service station is achieved. At last, we present several numerical examples under some special cases to discuss the sensitivity of the steady-state unavailability and the failure frequency in the 2 type failure of the service station.